Questions tagged [dirichlet-distribution]
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
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Mapping two Dirichlet Distributions into a comparative Dirichlet
Assume I observe some draws from 2 choice options, and want to infer the probabilities of various outcomes, e.g. non-negative integers up to a limit L. I could simply use 2 Dirichlet distributions to ...
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What is a representation of positive numbers summing to one that can be sampled via HMC?
I have a probability density $f(x): \mathbb{R}^n \rightarrow \mathbb{R}$ whose argument vector $x$ satisfies the constraints that all elements are positive and sum to unity. I need to generate samples ...
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Zero-Inflated Dirichlet
I want to set up a model that will rely on something similar to a zero-inflated Dirichlet distribution. As such, I'm trying to figure out how a zero-inflated Dirichlet distribution is set up from the ...
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How to calculate the expectation of the following Dirichlet distribution and Beta distribution?
This is a question from my research, related to the derivation of the variational EM algorithm with mean-field assumption about LDA-based model.
We all know, given that $\boldsymbol{\theta} \sim \...
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How to derive the expectation of $\log[a \theta_k + b]$ in Dirichlet distribution?
Given that $\boldsymbol{\theta} \sim \mathrm{Dir}(\boldsymbol{\alpha})$, then $E_{p(\boldsymbol{\theta} \mid \boldsymbol{\alpha})}[\log{\theta_k}] = \Psi(\alpha_k) - \Psi(\sum_{k'=1}^K \alpha_{k'})$, ...
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Sampling quantities with a fixed sum ("string cutting"), but those quantities have to be discrete
I would like to sample 6 quantities that are guaranteed to add up to 600, each with a mean of 100. I want to be control the amount of variance around 100 (same variance for all 6 quantities, but need ...
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Dirichlet/multinomial dirichlet model with autocorrelation
I need to estimate an inferential statistical model of a variable that is a set of 8 proportions that sum to 1. The data repeat for 25 years and the series is an AR1 process. Is there a statistical ...
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Results dirichlet regression - brms vs DirichelReg comparison
I am new to Dirichlet regression, but I am trying to understand why model outputs are potentially different when I use two different R packages, and how I could interpret the slope and intercept ...
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Choosing a probability distribution for 4D data: dirichlet challenges and alternatives
I'm seeking the right distribution for my 4D data, where the sum of values in each sample equals one. Currently, I've chosen to employ the Dirichlet distribution. However, upon applying this ...
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Do you know if this re-scaled Dirichlet kernel is known in the literature? How to sample from it?
In a Bayesian analysis, I came across the following distribution that results ends up looking like a re-scaled Dirichlet distribution. The motivation comes from looking at probabilities $x_1, \ldots, ...
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Dirichlet distribution with correlated components?
I am working with models that use Dirichlet distributions. However, I want to account for correlations between components. If this question is a duplicate, I'd also appreciate any pointers to the ...
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A confusion about computing transformation of random variables
Let $(X,Y)$ be a pair of random variables with joint pdf $f_{XY}$. Let $(U,V)$ be two random variables obtained from $(X,Y)$ by $U = u(X,Y)$ and $V = v(X,Y)$ where $u$ and $v$ are, say, nice ...
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number of parameters in Dirichlet Mixture Model clustering (non-bayesian)
I made a function that implements the clustering algorithm in the research article "Clustering compositional data using Dirichlet mixture model" (2022). I am now trying to figure out which ...
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Dirichlet distribution centered at a gaussian random field?
I created three (100x100) synthetic images using values randomly drawn from a Dirichlet distribution as shown below. Each image represent the abundance values of some surface components (soil, water ...
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Power of Uniform Order Statistics
I know that if $U$ is a uniform r.v. in $(0,1)$, then $U^a\sim Beta(1/a,1)$ with $a>0$.
On the other hand, if $U_{(1)}\leq \cdots\leq U_{(n)}$ are the uniform order statistics, then, with $U_{(0)}=...
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